How did Victor happen to be brought up with Elizabeth in the story Frankenstein?

Elizabeth is a little girl that Frankenstein's mother instantly falls in love with. Victor and his mother are helping the less fortunate one day when they come to a small cottage. Upon entering it they both instantly develop an affinity for the little child with blond hair and blue eyes. Mrs. Frankenstein asks the mother of the family where the child came from and the mother hastily replies that she is an orphan. The Frankenstein's end up adopting the angelic child.